Functions/Michaela P. Summary: In this unit, you will learn about functions. Some skills you will need before you begin this unit are graphing and order of operations. By the end of this unit, you should be able to tell the difference between a function and relation, identify both domain and range, graph a linear function, and solve a linear function. There are several key pieces of information presented in this unit. They include: the definitions of the word function, range, and domain, the input and output of an equation, the different ways a function can be presented, the vertical line test, function notation, and asymptotes. One common misconception to look out for in this unit includes thinking that if the two inputs have the output it is not a function. The opposite is true. If the same input has two outputs, than it is not a function. Another common mistake people make is confusing domain and range. Generally, in this unit, word problems are the most challenging. This is because you have to figure out all the little details from only a couple of sentences and then solve. For these, you just have to slow down and take your time. Rushing could cause you to make a small mistake that messes up your entire equation.
Created Problems: 1. Identify the domain and range of the function below a. Domain: x exists in the set of all real numbers Range: y-1
2. f(x)=5x+3 f(4) f(4)=5(4)+3 f(4)=20+3 a. f(4)=23
Applications:
Algebra 2: Use the following function rule to find f(2). f(x)=2x+3 f(2)=2(2)+3 f(2)=4+3 f(2)=7 This problem is from an algebra 2 website. To get the answer, you substitute the x for 2, both in the function notation and in the equation. After that you solve the problem like any other. You multiply the two 2s, and then add the 3.
SAT/ACT: What is the domain of the set of ordered pairs: {(2,-3), (4,6), (-3,5), (-2,5)}? Domain: {-3,-2,2,4} This problem is from an SAT practice website. To find the domain, you have to look at all the x-values and list them in order from least to greatest.
Real Life: A car rental charge is $100 per day plus $0.30 per mile travelled. Determine the equation of the line that represents the daily cost by the number of miles travelled. If a total of 300 miles was travelled in one day, how much is the rental company going to receive as a payment? f(x)=.3x+100 f(300)=.3(300)+100 f(300)=90+100 f(300)=190 The rental car company will receive $190. This is an example of how you can use function in real life. The equation is a simple y=mx+b equation with the y replaced by f(x). As for solving, you input 300 for all the xs and simply follow PEMDAS. You multiply .3 by 300, and add that to 100.
Summary:
In this unit, you will learn about functions. Some skills you will need before you begin this unit are graphing and order of operations. By the end of this unit, you should be able to tell the difference between a function and relation, identify both domain and range, graph a linear function, and solve a linear function. There are several key pieces of information presented in this unit. They include: the definitions of the word function, range, and domain, the input and output of an equation, the different ways a function can be presented, the vertical line test, function notation, and asymptotes. One common misconception to look out for in this unit includes thinking that if the two inputs have the output it is not a function. The opposite is true. If the same input has two outputs, than it is not a function. Another common mistake people make is confusing domain and range. Generally, in this unit, word problems are the most challenging. This is because you have to figure out all the little details from only a couple of sentences and then solve. For these, you just have to slow down and take your time. Rushing could cause you to make a small mistake that messes up your entire equation.
Created Problems:
1. Identify the domain and range of the function below
a. Domain: x exists in the set of all real numbers
Range: y-1
2. f(x)=5x+3 f(4)
f(4)=5(4)+3
f(4)=20+3
a. f(4)=23
Applications:
Algebra 2:
Use the following function rule to find f(2).
f(x)=2x+3
f(2)=2(2)+3
f(2)=4+3
f(2)=7
This problem is from an algebra 2 website. To get the answer, you substitute the x for 2, both in the function notation and in the equation. After that you solve the problem like any other. You multiply the two 2s, and then add the 3.
SAT/ACT:
What is the domain of the set of ordered pairs: {(2,-3), (4,6), (-3,5), (-2,5)}?
Domain: {-3,-2,2,4}
This problem is from an SAT practice website. To find the domain, you have to look at all the x-values and list them in order from least to greatest.
Real Life:
A car rental charge is $100 per day plus $0.30 per mile travelled. Determine the equation of the line that represents the daily cost by the number of miles travelled. If a total of 300 miles was travelled in one day, how much is the rental company going to receive as a payment?
f(x)=.3x+100
f(300)=.3(300)+100
f(300)=90+100
f(300)=190
The rental car company will receive $190.
This is an example of how you can use function in real life. The equation is a simple y=mx+b equation with the y replaced by f(x). As for solving, you input 300 for all the xs and simply follow PEMDAS. You multiply .3 by 300, and add that to 100.